Question

27.
Prove that 2-√3 is irrational, given that √3 is irrational,​

Answer 1

Answer:

Given

3

is irrational number

Let 2+

3

is rational number.

then 2+

3

=

q

p

3

=

q

p−2q

Since

3

is irrational number but

q

p−2q

is rational it mean

irrational = rational

which contradict,

∴ our assumption is wrong and

2+

3

is irrational number.